The Canaries won there first match of 2003 and re-started there push for promotion with a Paul McVeigh second half strike against a nine men Blades.
City were eighth before today's game and moved into the top six as they capitalised with there numerical advantage after Wayne Quinn and Peter Ndlovu where both sent off.
The result also meant that United had lost there fourth successive league defeat home and away.
It was the Blades who had the first chance which came in sixth minute, Peter Ndlovu fired in from edge of the box but Robert Green got down well to save.
Though Norwich moments later almost took the lead against the run of play when on loan striker David Healy shot which Paddy Kenny pushed around the post.
Another chance fell Canaries way when Clint Easton (who was celebrating his 250th appearance) swung the ball into the area where Welsh International Iwan Roberts headed but Kenny denied the forward of a goal.
Healy was a becoming a menace to the United defenders and was denied on two occasions by Kenny, Iwan Roberts once again produced a shot while Kenny saved again and the young goalkeeper later denied Steen Nedergaard. United battled on and on but the Wayne Quinn sending off proved to be a crucial part of the game.
Quinn, who is on loan from Newcastle United was dismissed for a second bookable offence on the hour mark after a late but not dangerous challenge on Healy but nine minutes later Paul McVeight scored the winning goal.
McVeigh a Northern International weaved his way round before stabbing the ball home past Paddy Kenny who did not stand a chance of saving it.
Zimbabwean International Peter Ndlovu was later sent off for a second book able offence to cap a miserable day for United.
Full Time: Sheffield United 0-1 Norwich City